Question

rewrite the rational expression as the sum of a quotient and a fractional remainder by long division. (\frac{3x^3 - 2x + 4}{x - 2}) use the keypad to enter the answer in the box. (\frac{3x^3 - 2x + 4}{x - 2} = square)

Explanation:

Step1: Divide leading terms

$\frac{3x^3}{x} = 3x^2$
Multiply divisor by $3x^2$: $3x^2(x-2)=3x^3-6x^2$
Subtract from dividend:
$(3x^3-2x+4)-(3x^3-6x^2)=6x^2-2x+4$

Step2: Divide new leading terms

$\frac{6x^2}{x}=6x$
Multiply divisor by $6x$: $6x(x-2)=6x^2-12x$
Subtract:
$(6x^2-2x+4)-(6x^2-12x)=10x+4$

Step3: Divide new leading terms

$\frac{10x}{x}=10$
Multiply divisor by $10$: $10(x-2)=10x-20$
Subtract:
$(10x+4)-(10x-20)=24$

Step4: Combine quotient and remainder

Quotient: $3x^2+6x+10$, remainder: $24$
Expression: $3x^2+6x+10+\frac{24}{x-2}$

Answer:

$3x^2+6x+10+\frac{24}{x-2}$